Question: Multiply the following complex numbers: $({-4+3i}) \cdot ({5+i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-4+3i}) \cdot ({5+i}) = $ $ ({-4} \cdot {5}) + ({-4} \cdot {1}i) + ({3}i \cdot {5}) + ({3}i \cdot {1}i) $ Then simplify the terms: $ (-20) + (-4i) + (15i) + (3 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -20 + (-4 + 15)i + 3i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -20 + (-4 + 15)i - 3 $ The result is simplified: $ (-20 - 3) + (11i) = -23+11i $